This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present invention. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present invention. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art.
An important goal of seismic prospecting is to accurately image subsurface structures commonly referred to as reflectors. Seismic prospecting is facilitated by obtaining raw seismic data during performance of a seismic survey. During a seismic survey, seismic energy is generated at ground level by, for example, a controlled explosion, and delivered to the earth. Seismic waves are reflected from underground structures and are received by a number of sensors referred to as geophones. The seismic data received by the geophones is processed in an effort to create an accurate mapping of the underground environment. The processed data is then examined with a goal of identifying geological formations that may contain hydrocarbons.
Full Wavefield Inversion (FWI) is a geophysical method which is used to estimate subsurface properties (such as velocity or density). It is known to be advanced for the higher resolution and more accurate physics compared to conventional methods. The fundamental components of an FWI algorithm can be described as follows: using a starting subsurface physical properties model, synthetic seismic data are generated by solving a wave equation using a numerical scheme (e.g., finite-difference, finite-element etc.). The synthetic seismic data are compared with the field seismic data and using the difference between the two, the value of an objective function is calculated. To minimize the objective function, a modified subsurface model is generated which is used to simulate a new set of synthetic seismic data. This new set of synthetic seismic data is compared with the field data to recalculate the value of the objective function. The objective function optimization procedure is iterated by using the new updated model as the starting model for finding another search direction, which will then be used to perturb the model in order to better explain the observed data. The process continues until an updated model is found that satisfactorily explains the observed data. A global or local optimization method can be used to minimize the objective function and to update the subsurface model. Commonly used local objective function optimization methods include, but are not limited to, gradient search, conjugate gradients, quasi-Newton, Gauss-Newton and Newton's method. Commonly used global methods included, but are not limited to, Monte Carlo or grid search.
Although FWI is expected to provide the subsurface properties, it is difficult to extract the correct viscoelastic properties from the seismic data directly with FWI. As FWI estimates the properties by fitting the data with synthetic waveforms, it relies on how accurate the wave equation can explain the actual physics, and how well the optimization method can separate the effects from different properties. When an acoustic wave equation is used, FWI can generate P-wave velocity models based on the travel time information in the datasets. However, the amplitude information is not fully utilized because the real earth is visco-elastic, and an acoustic model cannot explain all the amplitudes in the acquired data. If FWI is expected to provide interpretable products like elastic impedances, elastic simulation is often needed but very expensive; in general it is 6 to 10 times the computation of acoustic FWI. In addition, the initial model for shear wave velocity is difficult to obtain due to the limited shear wave kinematic information and often poor signal to noise ratio in the acquisitions.
An alternative way of using the elastic amplitude information is to form angle stacks. Amplitude versus angle (AVA) analysis [5] can be performed on the angle stacks to extract the elastic properties. Traditional AVA stacks generated with Kirchhoff migration need geometric spreading corrections to account for the amplitude loss during propagation. However, it is not guaranteed that the amplitude after correction would reflect the true amplitude of the data. In addition, Kirchhoff migration is based on ray-tracing which favors smooth velocity models and would likely fail in high contrast medium. Angle calculations are under a 1-D assumption that is not accurate enough when subsurface structures are complex. Reverse time migration (RTM) based angle stacks [1, 2] are more advanced for making use of the high-resolution velocity models. Nonetheless, amplitude preservation is still difficult. Yu Zhang et al (2014) [3] reported a least-squares RTM to balance the image amplitudes; however, it has not been proved to be able to generate angle stacks.